Question

Isotopes are separated by a mass spectrometer.  Ions are accelerated through a potential difference and then allowed to pass through a velocity selector.  The velocity selector is composed of a uniform 0.0500 T magnetic field and a uniform electric field perpendicular to each other.  If the electric field is produced using parallel plates that are 2.50 cm apart, what is the potential difference between the plates that will permit singly charged ions with a speed of 3.28 x 10⁵ m/s to pass undeflected through the selector? 

Answer 1

Velocity vector, E = vB for parallel plates with singly charge V = Ed.

Where, E = electric field between the plates.

            v = Velocity sector.

            B =magnetic field.

            d = Distance between the plates.

            V = potential difference between the plates.

Substitute the values : v = 3.28 × 105 m/s and B = 0.0500T in E = vB.

E = vB

E = (3.28 × 105) * (0.0500T) = 17.22V/m.

Substitute the values : E = 17.22 V/m and d = 2.50cm = 2.50 × 10^-2 m in V = Ed.

V = Ed

V = (17.22) * (2.50 × 10^-2 )

V = 43.05 × 10^-1

V = 4.305 v.

Therefore,the potential difference between the plates is 4.305 v.